Asked by Allie
what does factoring the sum or difference of two cubes mean
Answers
Answered by
Steve
It means using the handy known factorizations, as in
(a^3+b^3) = (a+b)(a^2-ab+b^2)
(a^3-b^3) = (a-b)(a^2+ab+b^2)
Of course, only the sum is needed, since
(a^3-b^3) = (a^3+(-b)^3)
once you recognize the sum of two cubes, like
125x^6+216/z^9
where
a = 5x^2
b = 6/z^3
just plug into the formula
125x^6 + 216/z^9 = (5x^2+6/z)(25x^4-30x^2/z^3+36/z^6)
so, it helps to know your cubes of small numbers, and watch for exponents which are multiples of 3.
(a^3+b^3) = (a+b)(a^2-ab+b^2)
(a^3-b^3) = (a-b)(a^2+ab+b^2)
Of course, only the sum is needed, since
(a^3-b^3) = (a^3+(-b)^3)
once you recognize the sum of two cubes, like
125x^6+216/z^9
where
a = 5x^2
b = 6/z^3
just plug into the formula
125x^6 + 216/z^9 = (5x^2+6/z)(25x^4-30x^2/z^3+36/z^6)
so, it helps to know your cubes of small numbers, and watch for exponents which are multiples of 3.
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